Long story short, I will be medically releasing from the forces soon and plan to go back to trade school. I do not have the greatest credit score and I am wondering how much of an effect this will have on me finding suitable civilian employment. Can anyone with similar experience give me some insight on this?

Depends on job and employer and the reason why your credit score is low. Did you miss payments or declare bankruptcy? Then places like financial institutions likely won't look at you. Is your credit score low because you have not had much credit to build it?

Nah, its bad because I neglected to pay bills while I was going through a really rough period. It is starting to build back up (as I build up myself) but it will likely take at least a few years to replace the damage. I would not be looking to work for a financial institution, rather something more hands on like mechanic.

Employers tend not to look at credit scores, unless you will be working with money, like a bank, mortgage broker, etc. Or there is some level of security clearance that is involved, like with the police. But if you plan on being a mechanic, you should be fine